Matrix theory and Calculus are two classical and fundamental mathematical tools in modern science and technology. There are two mostly used operators on the set of matrices: conventional matrix product and matrix addition. Roughly speaking, the object of matrix theory is \(({\mathcal {M}},~+,~\times )\) , where \({\mathcal {M}}\)  is the set of all matrices. Unfortunately, unlike the arithmetic system \(({\mathbb {R}},~+,~\times )\) , in matrix theory both “\(+\) " and “\(\times \) " are restricted by the matrix dimensions. Precisely speaking: consider two matrices \(A\in {\mathcal {M}}_{m\times n}\)  and \(B\in {\mathcal {M}}_{p\times q}\) . Then the “product", \(A\times B\) , is well posed, if and only if, \(n=p\) ; the “addition" \(A+B\) , is defined, if and only if, \(m=p\)  and \(n=q\) . Though there are some other matrix products such as Kronecker product, Hadamard product etc., but they are of different stories [1]}.
